Decorrelating, linear, minimum mean-squared error (LMMSE), and noise-whitening multiuser detectors for code-division multiple-access systems (CDMA) are ideally infinite memory-length (referred to as IIR) detectors. To obtain practical detectors, which have low implementation complexity and are suitable for CDMA systems with time-variant system parameters (e.g., the number of users, the delays of users, and the signature waveforms), linear finite-memory-length (referred to as FIR) multiuser detectors are studied in this paper. They are obtained by truncating the IIR detectors or by finding optimal FIR detectors. The signature waveforms are not restricted to be time-invariant (periodic over symbol interval). Thus, linear multiuser detection is generalized to systems with spreading sequences longer than the symbol interval. Conditions for the stability of the truncated detectors are discussed. Stable truncated detectors are shown to be near-far resistant if the received powers are upper bounded, and if the memory length is large enough (but finite). Numerical examples demonstrate that moderate memory lengths are sufficient to obtain the performance of the IIR detectors even with a severe near-far problem.